Downing Street, which said the decision not to reappoint Baroness Morgan for a second three-year term had been made by Mr Gove, insisted the government "appoints people on merit".

'Game-playing'

The decision to get rid of Sally Morgan had absolutely nothing to do with her abilitiesSource close to Mr Laws

The outgoing chairwoman, who was appointed by the coalition in 2010 as chair of the education inspectorate for England, told BBC News her removal was part of a pattern which had seen a series of non-Conservative supporters on bodies like the Arts Council and the Charity Commission replaced with loyal Tories.

"I really do think it's just I am the latest of a fairly long list of people now who are non-Conservative supporters who are not being reappointed," she said.

"Often they are people who have been working really well with their organisations and, indeed, with their host departments, so I do think this is coming from Number 10.

"I don't think it is coming from individual departments."

A source close to Mr Laws told the BBC: "David is absolutely furious at the blatant attempts by the Tories to politicise Ofsted.

"The decision to get rid of Sally Morgan had absolutely nothing to do with her abilities, or even education policy, and everything to do with Michael Gove's desire to get his own people on board.

"David Laws is absolutely determined not to let Michael undermine the independence of this vital part of the education system.

"David's primary concern now is not to let Conservative game-playing destabilise Ofsted and he'll be working closely with them as schools minister to make sure that doesn't happen."

'Michael Gove's decision'

Downing Street said the claim it was involved in an effort to recruit Conservative sympathisers to public bodies was baseless.

"Michael Gove has thanked Sally Morgan for her effective and long service as chair of Ofsted. The decision not to reappoint her was his decision," a Number 10 spokesman said.

Baroness Morgan is a former aide to Tony Blair

"This government appoints people on merit: for example, Sally Morgan was herself appointed under this government; and the former Labour adviser Simon Stevens is about to take up the post of Chief Executive of NHS England."

The spokesman said Downing Street had also asked former Labour cabinet ministers to carry out independent reviews on key public policy issues, including Alan Milburn on social mobility and John Hutton on public service pensions.

In a statement, Ofsted said Baroness Morgan's term of office "has been extended until the autumn of 2014 by the secretary of state while the process is put in place to find a successor".

The row comes days after the education secretary denied claims by Sir Michael Wilshaw, the chief inspector of schools in England, that the Department for Education had briefed against Ofsted.